Nicking wires in a cable - how possible?

[Tigers!]

Last week I had to terminate 6 x cat6 ethernet cables.
In four of them I manged to nick and damage wire 5.
(From this I conclude that I need more practice.)

I was wondering how likely was that series of events? The sheath of the cables was black and could not show the wires inside. I assume that it will be random as to where around the cable that I will start cutting the sheath.

The probability of nicking a wire is 1/8.
To chose any four cables out of 6 is 4C6 = 15 possible combinations

So I concluded that the probability of nicking a wire in 8 in 4 out of 6 cables = (1/8)/(1/15) = 0.0666666....

But that does not tell me what is the probability of nicking the same wire in the cables

I am not sure how to express that.

What would need to change in the calculation?

 

[bilby]

Nicking a wire isn't a random event; it's likelihood is determined not be chance, but by your level of (in)competence.

Given that four of six cables ended up with one (and only one) nicked wire, as a consequence of your (in)ability; And given that you couldn't see which wire you were nicking, the pattern of which wires got nicked is probabilistic. With four 1/8 chances at any given wire, the probability of getting any given pattern in a specified order is the same for any pattern - nicking wires 4, 4, 4, and 4 is exactly as likely as nicking wires 4, 6, 7, and 3 - it appears remarkable only because humans are naturally inclined to look for patterns and assign significance to them.

But each possible combination is equally likely. And the probability of a given combination after the event is 1.